Laminated beams with time-varying delay

Abstract

This manuscript is concerned with long-time dynamics for a laminated beam which consists of two identical layers of uniform thickness, taking into account that an adhesive of small thickness is bonding the two surfaces thereby producing an interfacial slip. Using the variable norm technique of Kato, we prove the global well-posedness of solutions. For asymptotic behavior, we apply the Energy Method. Assuming the control through a time-varying delay just on the transverse displacement of the beam, we establish the exponential decay of energy to the system by using an appropriate Lyapunov functional.